The standard solution concept for Bayesian games is the Bayes-Nash equilibrium (BNE), which generalizes the notion of a NE. However, the NE already suffers from several problems.
[1]} showed that finding NE is PPAD complete, and [2]} demonstrated that it is hard to approximate. Furthermore, a single game can have many different NE, leading to the equilibrium selection problem [3]}. These issues make the BNE or NE challenging.
[4]} studied the stability of NE under perturbations of the players' strategies and introduced the notion of trembling hand. One defines a sequence of perturbed games, where each player has to play all available strategies with at least a probability of \(\epsilon _n\) . With \(\epsilon _n \rightarrow 0\) , one observes the NE in the perturbed games. If a sequence of NE exists in the perturbed games that converge to a NE in the original game, this NE is said to be a trembling hand perfect NE. Unlike the NE, a trembling hand perfect NE is stable under small changes in the vNM values. However, it still suffers from intractability and multiplicity [5]}.
